Many devices that employ magnetic fields have heretofore been encumbered by massive solenoids with their equally bulky power supplies. Thus, there has been increasing interest in the application of permanent-magnet structures for such uses as electron-beam focusing and biasing fields. The current demand for compact, strong, static magnetic field sources that require no electric power supplies has created needs for permanent magnet structures of unusual form. A number of configurations have been designed and developed for electron-beam guidance in mm/microwave tubes of various types; for dc biasing fields in millimeter wave filters, circulators, isolators, strip-lines; for field sources in NMR (nuclear magnetic resonance) imagers; and so on. Especially promising for such purposes is the configuration based on the hollow cylindrical flux source (HCFS) principle described by K. Halbach, in "Proceedings of the Eighth International Workshop on Rare Earth Cobalt Permanent Magnets" (University of Dayton, Dayton, Ohio, 1985) p. 123-136. A HCFS, sometimes called a "magic ring", is a cylindrical permanent-magnet shell which offers a magnetization vector that is more-or-less constant in magnitude and produces a field greater than the remanence of the magnetic material from which it is made.
The "magic ring" or HCFS concept has proven to be useful for a variety of applications that require relatively high transverse fields in tubular working spaces (e.g., mm/microwave radiation sources and amplifiers). Unfortunately, there are field distortions in the magic ring due to end effects, and to achieve a fairly uniform biasing field the device would have to be wastefully long (i.e., a very large length-to-radius ratio). And, the length necessary to achieve a highly uniform biasing field requires a fairly massive structure.